Method of accelerating simultaneous localization and mapping (slam) and device using same

ABSTRACT

A preconditioned conjugate gradient (PCG) solver, embedded in an electronic device to perform a simultaneous localization and mapping (SLAM) operation, includes an image database, a factor graph database, and a back-end processor, wherein the back-end processor is configured to receive an image from the image database to perform re-localization, receive, from the factor graph database, data for calculating six degrees of freedom (DoF)-related components, construct a matrix including the six degrees of freedom-related components based on the received data, and load and rearrange the matrix and a vector, to perform calculation on each block of each row of the matrix and the vector, then output first data, and shift second data to a location of the first data.

CROSS-REFERENCE TO RELATED APPLICATION

This application is based on and claims priority under 35 U.S.C. § 119to Korean Patent Application No. 10-2020-0148128, filed on Nov. 6, 2020,in the Korean Intellectual Property Office, the disclosure of which isincorporated by reference herein in its entirety.

BACKGROUND 1. Field

Apparatuses and methods consistent with example embodiments relate toaccelerating matrix operations to shorten processes of performingsimultaneous localization and mapping (SLAM), and a device using thesame.

2. Description of the Related Art

In order to construct a map in a virtual space, a process of analyzingan image received from a camera or the like and determining coordinatesis required. Implementation of a virtual space represented by augmentedreality (AR) and virtual reality (VR) may be achieved by using aportable device, for example, glasses (for example, AR glasses).

Simultaneous localization and mapping (SLAM) may refer to a technologyfor constructing a map of a virtual space in real time. Various devicesmay update a map of a virtual space in real time by using SLAM, andrapid calculation may be required to respond to movement of a user usingthe devices.

SUMMARY

SLAM may be implemented by a front end processor to receive sensorinformation and perform feature extraction and spatial coordinatecalculation, and a back end processor to optimize map information andcurrent position information based on an output of the front endprocessor. The front end may be implemented mainly by using visualodometry based on camera information and an inertial navigation system(INS) using an inertial measurement unit (IMU), and various sensorfusion schemes may be applied according to types of the front endprocessor. In a case where the back end processor optimizes locationinformation generated based on sensor data, together with map data, anamount of mathematical operations may greatly increase according to asize of a map, and a size and accuracy of the sensor data.

Generally, SLAM may be implemented with a combination of multiplecameras and an IMU, and mathematical operations for SLAM may beperformed by processors having various performance specifications onvarious platforms. In particular, optimization of the back end processorrequires a large amount of mathematical operations and may greatlyaffect the entire performance of SLAM.

SLAM, to be combined with a virtual space, may be configured to havelow-power consumption to improve the wearability of a device implementedwith SLAM. In a case of a low-power, low-performance back-end processor,processing of the mathematical operations may take a long time. Also, ina case of tethered SLAM for connection with a mobile device, problemsdue to the weight of wires for connection between devices or datalatency may occur. A device (e.g., AR glasses) embedded with ahigh-performance processor may increase its size and power consumption.

According to an aspect of an example embodiment, there is provided anelectronic device to perform a simultaneous localization and mapping(SLAM) operation, the electronic device including: an image database; afactor graph database; and a processor configured to: receive, from theimage database, a map image in which a position of the electronic deviceis localized, to perform re-localization of the position of theelectronic device in the map image; receive, from the factor graphdatabase, data for calculating six degrees of freedom (DoF)-relatedcomponents of the electronic device; construct a matrix including thesix DoF-related components based on the received data; and load andrearrange the matrix and a vector that is selected from a plurality ofvectors stored in a memory, to sequentially obtain first data and seconddata by performing calculation on each block of each row of the matrixand the vector, and shift the second data to a storage location of thefirst data.

The processor may be further configured to reuse as many elements as asize of the block in the calculation of the matrix and the vector.

The processor may be further configured to calculate only diagonalelements of the matrix by using properties of a scattering matrix thatis derived from the map image and the data for calculating the sixDoF-related components.

The processor may be further configured to calculate as many transposeelements as a maximum size of each row block in the calculationperformed on each block of each row of the constructed matrix.

The processor may be further configured to output the shifted seconddata, and accumulate the second data and the first data.

The processor may be further configured to simultaneously performaccumulation of the first data and the second data, and shifting of thesecond data.

The processor may be further configured to perform the shifting of thesecond data by using a shift register.

Elements of the constructed matrix may include a position component, arotation component, a linear velocity component, an accelerationcomponent, and an angular velocity component with respect to three axesof the electronic device.

The processor may be further configured to control an interval between afirst output time of the first data and a second output time of thesecond data according to a preset period.

The image database may store an image received from a camera of theelectronic device.

According to an aspect of an example embodiment, there is provided amethod of accelerating simultaneous localization and mapping (SLAM)performed by an electronic device, including: receiving, from an imagedatabase, a map image in which a position of the electronic device islocalized, to perform re-localization of the position of the electronicdevice in the map image; receiving, from a factor graph database of theelectronic device, data for calculating six degrees of freedom(DoF)-related components of the electronic device; constructing a matrixincluding the six DoF-related components based on the received data; andloading and rearranging the matrix and a vector that is selected from aplurality of vectors stored in a memory, to sequentially obtain firstdata and second data by performing calculation on each block of each rowof the matrix and the vector, and then shift the second data to astorage location of the first data.

The method may further include reusing as many elements as a size of theblock in the calculation performed on the matrix and the vector.

The method may further include calculating only diagonal elements of thematrix by using properties of a scattering matrix that is derived fromthe map image and the data for calculating the six DoF-relatedcomponents.

The method may further include calculating as many transpose elements asa maximum size of each row block in the calculation performed on eachblock of each row of the constructed matrix.

The method may further include outputting the shifted second data, andaccumulating the second data and the first data.

The outputting of the second data may include simultaneously performingaccumulation of the first data and the second data, and shifting of thesecond data.

The method may further include performing the shifting of the seconddata by using a shift register.

The constructing of the matrix may include calculating a positioncomponent, a rotation component, a linear velocity component, anacceleration component, and an angular velocity component of the matrixwith respect to three axes of the electronic device.

The method may further include controlling an interval between a firstoutput time of the first data and a second output time of the seconddata according to a preset period.

The method may further include storing, in the image database, the mapimage that is generated based on an image received from a camera of theelectronic device.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and/or other aspects will be more apparent by describingcertain example embodiments, with reference to the accompanyingdrawings, in which:

FIG. 1 is a block diagram illustrating components of a preconditionedconjugate gradient (PCG) solver, according to various embodiments;

FIG. 2 is an exemplary diagram illustrating a configuration of a PCGsolver, according to various embodiments;

FIG. 3 is an exemplary diagram illustrating a matrix-vector selector,according to various embodiments;

FIG. 4 is an exemplary diagram illustrating a matrix-vector multiplier,according to various embodiments;

FIG. 5 is an exemplary diagram illustrating a matrix-vector accumulator,according to various embodiments;

FIG. 6 is a flowchart of data operations performed by a PCG solver andtheir outputs, according to various embodiments;

FIG. 7 is a flowchart of mathematical operations performed by a PCGsolver, according to various embodiments;

FIG. 8 is an exemplary diagram related to mathematical operationsperformed by a PCG solver and their outputs, according to variousembodiments; and

FIG. 9 is an exemplary diagram related to mathematical operationsimplification and resulting outputs of a PCG solver, according tovarious embodiments.

DETAILED DESCRIPTION

Example embodiments are described in greater detail below with referenceto the accompanying drawings.

In the following description, like drawing reference numerals are usedfor like elements, even in different drawings. The matters defined inthe description, such as detailed construction and elements, areprovided to assist in a comprehensive understanding of the exampleembodiments. However, it is apparent that the example embodiments can bepracticed without those specifically defined matters. Also, well-knownfunctions or constructions are not described in detail since they wouldobscure the description with unnecessary detail.

As used herein, the term “and/or” includes any and all combinations ofone or more of the associated listed items. Expressions such as “atleast one of,” when preceding a list of elements, modify the entire listof elements and do not modify the individual elements of the list. Forexample, the expression, “at least one of a, b, and c,” should beunderstood as including only a, only b, only c, both a and b, both a andc, both b and c, all of a, b, and c, or any variations of theaforementioned examples.

The terms used in the embodiments are selected from among common termsthat are currently widely used, however, the terms may be differentaccording to an intention of one of ordinary skill in the art, aprecedent, or the advent of new technology. Also, in particular cases,the terms are discretionally selected by the applicant of the presentdisclosure, in which case, the meaning of those terms will be describedin detail in the corresponding part of the detailed description.Therefore, the terms used in the present disclosure are not merelydesignations of the terms, but the terms are defined based on themeaning of the terms and content throughout the present disclosure.

The terms such as “include” or “comprise” used herein should not beconstrued as necessarily including all various elements or operationsdescribed herein and should be understood that some of the elements oroperations may be omitted or additional elements or operations may befurther provided.

In the embodiments, it will be understood that when an element isreferred to as being “connected to” another element, the element may bedirectly connected to another element or may be electrically connectedto another element while having intervening elements therebetween.

It will be understood that, although the terms such as “first” or“second” may be used herein to describe various elements, these elementsshould not be limited by these terms. These terms are only used todistinguish one element from another element.

FIG. 1 is a block diagram illustrating elements of a preconditionedconjugate gradient (PCG) solver included in an electronic device,according to various embodiments.

Referring to FIG. 1, a PCG solver 100 may include a back-end processor110, an image database 120, and a factor graph database 130. Forexample, the PCG solver 100 may perform complicated multiplicationoperations of matrices. The PCG solver 100 may perform a multiplicationoperation of a matrix and/or a vector repeatedly performed. For example,the PCG solver 100 may accelerate execution of SLAM. The PCG solver 100may efficiently process the multiplication operation of a matrix and/ora vector thereby enabling a back end processor to perform SLAM rapidly.Referring to FIG. 1, the components of the PCG solver 100 are merelyexemplary and not limited thereto, and some of the elements may besubstituted and/or additional elements may be further included.

Simultaneous localization and mapping (SLAM) is a technique forsimultaneously performing positioning and map construction. For example,various electronic devices may perform SLAM to estimate their positionin real time and construct maps of their environments. SLAM may includevisual SLAM. For example, visual SLAM may include a visual odometrysystem. The visual odometry system may calculate and accumulate relativepositions of the electronic device for every frame. For example, thevisual odometry system may calculate positions of the electronic devicein real time, from a starting point at which the electronic devicebegins to move. Because the visual odometry system performs thecalculation from an image received from a camera, an error may occur dueto noise of the received image. SLAM may utilize loop closure and graphoptimization in addition to the visual odometry system. For example,when the electronic device returns to the starting point, a trajectoryof the electronic device may be corrected by using a loop closuremethod.

Referring to FIG. 1, the back-end processor 110 may perform mathematicaloperations for optimizing SLAM performed by the PCG solver 100. Forexample, the electronic device may include a front-end processorconfigured to receive sensory data that are derived from multiplesensors (e.g., cameras, light detection and ranging (LiDAR) devices,etc.) and perform sensor fusion to combine the sensory data derived fromthe multiple sensors. The back-end processor 110 may receive a result ofthe sensor fusion from the front-end processor, and calculate anaccumulated travel distance based on the result of the sensor fusion.The back-end processor 110 may receive data from the front-end processorand repeatedly perform a mathematical operation. For example, theback-end processor 110 may perform a mathematical operation on a matrixand/or a vector, to estimate a position of the electronic device andconstruct a map. The back-end processor 110 may estimate a position ofthe electronic device on the constructed map. For example, the back-endprocessor 110 may estimate a position of the electronic device that ismoving, on the constructed map, based on the mathematical operationsrepeatedly performed. The back-end processor 110 may estimate a positionof the electronic device in real time, and data related to the estimatedposition may be updated in real time. The first-end processor and theback-end processor 110 may be integrated into a single processor, or maybe implemented by separate processors.

The image database 120 may store an image received from an image signalprocessor (ISP). The image database 120 may transmit image data forperforming re-localization. For example, the back-end processor 110 mayreceive, from the image database 120, the image data necessary forperforming SLAM. The image database 120 may receive an image (e.g., amap image that shows an area including the location of the electronicdevice) from the image signal processor in real time and transmit, tothe back-end processor 110, the image data necessary for estimating aposition of the electronic device in real time. For example, theback-end processor 110 may receive the image data from the imagedatabase 120 as the electronic device moves, and may then performre-localization on the electronic device.

The factor graph database 130 may store data received from an inertialmeasurement unit (IMU). The IMU may be implemented by any one or anycombination of an accelerometer, a gyroscope, a magnetometer, and aglobal positioning system (GPS) sensor, and may measure the position,angular rate, and orientation of an object, For example, the factorgraph database 130 may store data related to triaxial coordinatesmeasured by the inertial measurement unit. The factor graph database 130may transmit data related to translational movements and rotationalmovements related to a triaxial movement of the electronic device. Forexample, the back-end processor 110 may receive, from the factor graphdatabase 130, data for calculating components related to six degrees offreedom (6 DoF) of the electronic device.

An electronic device embedded with the PCG solver 100 may include aninertial sensor, an acceleration sensor, an angular velocity sensor, amagnetic sensor, a geomagnetic sensor, etc. The electronic device, inwhich the acceleration sensor and the angular velocity sensor operatewith three axes orthogonal to each other, may be used as an IMU capableof detecting six degrees of freedom. For example, the back-end processor110 may receive detection outputs by the acceleration sensor and theangular velocity sensor of the electronic device, and then calculate arelative position of the electronic device based on a linearacceleration and an angular velocity with respect to the three axes. Theback-end processor 110 may calculate a rotation angle of a referencecoordinate system of the electronic device based on the angularvelocity, and calculate a velocity, that is, an integral of theacceleration, and calculate a position, that is, an integral of thevelocity.

FIG. 2 is an exemplary diagram illustrating a configuration of the PCGsolver 100, according to various embodiments.

Referring to FIG. 2, the PCG solver 200 may include blocks that performvarious functions. For example, the PCG solver 200 may include a statecontroller, a memory array, a pre-processing unit, a multiplier unit,and a post-processing unit. The configuration of the PCG solver 200shown in FIG. 2 is merely exemplary and not limited thereto, and some ofthe blocks may be omitted or substituted, and/or additional blocks maybe further included. The PCG solver 200 may include at least one of theconfiguration and/or functions of the PCG solver 100 shown in FIG. 1.

Referring to FIG. 2, a matrix and/or a vector may be selected from thememory array by the pre-processing unit, based on a matrix input to thePCG solver 200. For example, a matrix-vector selector 210 of thepre-processing unit may select a matrix and/or a vector by which theinput matrix is multiplied. In addition to matrix-vector selector 210, avector-scalar selector may select a vector and/or a scalar. For example,the vector-scalar selector may select a vector and/or a scalar by whichthe input matrix is multiplied.

Referring to FIG. 2, multiplying the matrix input to the PCG solver 200by the matrix and/or the vector selected by the matrix-vector selector210 may be performed by a matrix-vector multiplier 220. For example, thematrix-vector multiplier 220 may perform the multiplication operation ofthe input matrix with the matrix selected by the matrix-vector selector210. The matrix-vector multiplier 220 may also perform themultiplication operation of the input matrix with the vector selected bythe matrix-vector selector 210. For example, the matrix-vectormultiplier 220 may perform the multiplication operation of the inputmatrix with the vector selected by the vector-scalar selector. A vectorscalar multiplier 240 may perform the multiplication operation of theinput matrix with the scalar selected by the vector-scalar selector.

Referring to FIG. 2, the post-processing unit of the PCG solver 200 mayinclude a matrix-vector accumulator 230. For example, the matrix-vectoraccumulator 230 may accumulate, as an output, at least a portion of aresult of the multiplication operation performed by the matrix-vectormultiplier 220. The matrix-vector accumulator 230 may store at least aportion of the output, in the PCG solver 200 or a memory of theelectronic device embedded with the PCG solver 200. A scalar accumulatormay accumulate, as an output, at least a portion of the result of themultiplication operation performed by the vector scalar multiplier 240.A vector adder may perform addition of at least some of vectors of theresult of the multiplication operation performed by the vector scalarmultiplier 240. A preconditioned vector adder may perform addition of atleast some of vectors according to a predefined condition.

Referring to FIG. 2, a processing result by the post-processing unit ofthe PCG solver 200 may return to the memory array. For example, theelectronic device may estimate its position in real time by performingSLAM, and output data that has been used for the position estimation maybe reused as a new input to update the position in real time.

FIG. 3 is an exemplary diagram illustrating the matrix-vector selector210, according to various embodiments.

Referring to FIG. 3, the matrix-vector selector 210 may select a matrixby using matrix data S as an input. For example, the matrix data S maybe used to calculate a Hessian matrix with a Schur complement. Thematrix data S may be stored in a matrix data register 210 a.

Referring to FIG. 3, the matrix-vector selector 210 may select a vectorby using vector data b as an input. The vector data b may be input inthe form of a matrix and selected. For example, the vector data b may bestored in a vector register for a transpose matrix 210 b through vectorregisters (e.g., a vector register 1, a vector register 2, a vectorregister 3, and a vector register 4). The vector data b may also bestored in a vector register for an original matrix 210 c through thevector registers.

Referring to FIG. 3, the matrix-vector selector 210 may select a matrixand/or a vector for optimization of a SLAM operation of the PCG solver200. The optimization of the SLAM operation may mean acceleration of theSLAM operation. For example, the speed of the SLAM operation may dependon the processing speed of the multiplication operation of a matrixand/or a vector. In order to increase the processing speed of themultiplication operation of a matrix and/or a vector, pre-processing maybe performed on transpose elements of each row of the input matrix. Theback-end processor 110 of the PCG solver 200 may perform selection of amatrix and/or a vector for increasing the processing speed of themultiplication operation, by using the matrix-vector selector 210 whileperforming the pre-processing.

FIG. 4 is an exemplary diagram illustrating the matrix-vector multiplier220, according to various embodiments.

Referring to FIG. 4, the matrix-vector multiplier 220 may perform themultiplication operation of a matrix and/or a vector. For example, thematrix-vector multiplier 220 may perform the multiplication operation ofa matrix (e.g., a scattering matrix) stored in the matrix data register210 a with a vector stored in the vector register 210 c for an originalmatrix. The scattering matrix (S matrix) may correspond to a symmetricpositive definite (SPD) matrix. The matrix-vector multiplier 220 mayperform the multiplication operation of a matrix (e.g., S matrix) storedin the matrix data register 210 a with a vector stored in the vectorregister 210 b for a transpose matrix. The S matrix may contain, as itselements, a camera-related (triaxial) position, a camera-related(triaxial) rotation, an IMU-related (triaxial) linear velocity, anIMU-related (triaxial) acceleration, and an IMU-related (triaxial)angular velocity. The back-end processor (e.g., the back-end processor110 of FIG. 1) of the PCG solver (e.g., the PCG solver 100 of FIG. 1 orthe PCG solver 200 of FIG. 2) may configure the S matrix by using datareceived from the image database (e.g., the image database 120 ofFIG. 1) and the factor graph database (e.g., the factor graph database130 of FIG. 1).

Referring to FIG. 4, the matrix-vector multiplier 220 may include threesets each consisting of eighteen multipliers, three rounding andclipping units, and three adders. The matrix-vector multiplier 220 mayfurther include a data rearranger, eighteen sets each consisting ofthree multipliers, eighteen rounding and clipping units, and eighteenadders. For example, the numbers of multipliers and sets of multipliersin the matrix-vector multiplier 220 may depend on a size of a matrixand/or a vector on which the multiplication operation is performed. Thesize of the matrix and/or the vector may be represented by “n*n”.

When performing the multiplication operation with respect to a vectorstored in the vector register 210 c for an original matrix, thematrix-vector multiplier 220 may obtain a product having a size of n*1as a result of the multiplication operation of a matrix having a size ofn*n with a vector having a size of n*1. For example, the matrix-vectormultiplier 220 may perform eighteen multiplication operations and thenperform three significant addition operations. The significant additionmay mean that a result of the multiplication operation is not convergedto zero.

Referring to FIG. 4, the result of the multiplication operationperformed by the matrix-vector multiplier 220 may be stored in anoriginal matrix register or a transpose matrix register. For example,the result of the multiplication operation with respect to a vector foran original matrix may be stored in the original matrix register. Theresult of the multiplication operation with respect to a vector for atranspose matrix may be stored in the transpose matrix register. Thevector registers of FIGS. 3 and 4 may be the same. For example, thevector register 210 c for the original matrix of FIG. 3 may be the sameas the vector register 210 c for the original matrix of FIG. 4, and theoriginal matrix register of FIG. 4 may store the result of themultiplication operation related to data of the vector register 210 cfor the original matrix of FIG. 3. The vector register 210 b for thetranspose matrix of FIG. 3 may be the same as the vector register 210 bfor the transpose matrix of FIG. 4, and the transpose matrix register ofFIG. 4 may store the result of the multiplication operation related todata of the vector register 210 b for the transpose matrix of FIG. 3.

The numbers of multipliers, rounding and clipping units, adders, anddata rearrangers of the matrix-vector multiplier 220 may not be limitedto the numbers shown in FIG. 4. For example, an individual operationcomponent of the matrix-vector multiplier 220 may be determinedaccording to a size of a matrix and/or a vector on which themultiplication operation is performed.

FIG. 5 is an exemplary diagram illustrating the matrix-vectoraccumulator 230, according to various embodiments.

Referring to FIG. 5, the matrix-vector accumulator 230 may accumulate,as an output, at least a portion of a result of the multiplicationoperation performed by the matrix-vector multiplier 220. For example,the matrix-vector accumulator 230 may accumulate and store data of theoriginal matrix register and data of the transpose matrix register, inan output order. The matrix-vector accumulator 230 may accumulateresults output by the multiplication operation of a matrix and/or avector, in sequence.

Referring to FIG. 5, the matrix-vector accumulator 230 may separate dataof the transpose matrix register by using a data splitter. For example,the data splitter may split data of the product of the multiplicationoperation stored in the transpose matrix register such that each row isdefined as one block.

Referring to FIG. 5, the matrix-vector accumulator 230 may reuse thedata of the original matrix register and the data of the transposematrix register. For example, the matrix-vector accumulator 230 mayreuse the results that are accumulated and stored, to estimate theposition of the electronic device embedded with the PCG solver 200.

FIG. 6 is a flowchart of data operations performed by the PCG solver 200and their outputs, according to various embodiments.

Referring to FIG. 6, in operation 610, the PCG solver (e.g., the PCGsolver 100 of FIG. 1 or the PCG solver 200 of FIG. 2) may receive animage from the image database (e.g., the image database 120 of FIG. 1).For example, the image being received may have been stored in the imagedatabase after being received from the image signal processor. Theback-end processor of the PCG solver (e.g., the back-end processor 110of FIG. 1) may perform the mathematical operations for SLAM on imagesstored in the image database.

Referring to FIG. 6, in operation 620, the PCG solver may receive datafrom the factor graph database (e.g., the factor graph database 130 ofFIG. 1). For example, the factor graph database may store data forextracting six degrees of freedom-related components according to amotion of the electronic device by using the IMU. The back-end processorof the PCG solver may perform the mathematical operations for SLAM onthe images stored in the factor graph database.

Referring to FIG. 6, in operation 630, the PCG solver may performcalculation of the six degrees of freedom-related components forestimating the position of the electronic device. For example, the PCGsolver may perform the calculation of the six degrees of freedom-relatedcomponents by using the image and data received from the image databaseand the factor graph database. The six degrees of freedom-relatedcomponents for estimating the position of the electronic device may berelated to translational movements (e.g., forward and backward movementson the X-axis, left and right movements on the Y-axis, and up and downmovements on the Z-axis) and rotational movements (e.g., yaw rotation,pitch rotation, and roll rotation) with respect to three axes (e.g., anx axis, a y axis, and a z axis) of the electronic device. The back-endprocessor of the PCG solver may perform the calculation of the sixdegrees of freedom-related components by using the IMU consisting of theacceleration sensor, the angular velocity sensor, or the like, and acamera of the electronic device. For example, the six degrees offreedom-related components may include a position, a rotation, a linearvelocity, an acceleration, and an angular velocity with respect to thethree axes.

Referring to FIG. 6, in operation 640, the PCG solver may configure amatrix according to factors. For example, the PCG solver may configure amatrix according to fifteen factors by using the back-end processor. Thefifteen factors may be obtained by calculating the six degrees offreedom-related components.

Referring to FIG. 6, in operation 650, the PCG solver may performblockwise calculation of a matrix and a vector. For example, theback-end processor of the PCG solver may define a row of the matrix asone block. The back-end processor may perform a multiplication operationof a block of the matrix and a vector.

Referring to FIG. 6, in operation 660, the PCG solver may sequentiallyoutput and accumulate data about results of the multiplication operationof the matrix and the vector. For example, the back-end processor mayoutput a result of the multiplication operation of a first block of thematrix and the vector, as first data. The back-end processor may shiftresult data output after the first data is output, to a location inwhich the first data has been stored. For example, the back-endprocessor may shift a result of the multiplication operation of eachblock other than the first block, and the vector, to the location inwhich the output first data has been stored. The back-end processor maysimultaneously perform the outputting of the first data and the shiftingof the result of the multiplication operation of each block other thanthe first block, and the vector. In operations 660, the back-endprocessor may simultaneously perform the outputting of the first dataand shifting of nth data, wherein n denotes a natural number. The nthdata may be the second data. For example, the back-end processor mayshift the nth data to a location in which the first data was storedbefore being output, while outputting the first data to a register inwhich result values are accumulated. The location in which the firstdata was stored before being output may refer to a shift register. Inoperation 660, the first data and the nth data may be sequentiallyoutput and accumulated according to a calculation order of the back-endprocessor. The back-end processor may control the outputting of the nthdata after the outputting of the first data according to a presetperiod. For example, the preset period may be 0.1 seconds. In a case ofthe preset period being a low value, the back-end processor may perform,in real time, the outputting of the first data and the nth data thatcorrespond to result values of the calculation of the six degrees offreedom-related components of the electronic device embedded with thePCG solver.

FIG. 7 is a flowchart of mathematical operations performed by the PCGsolver 200, according to various embodiments.

Referring to FIG. 7, the PCG solver may perform the mathematicaloperations by using a matrix and a vector as inputs. In operation 701,the pre-processing unit of the PCG solver may receive a matrix S andvectors b and X₀, from the memory array, as inputs on which themathematical operations will be performed. For example, in operation702, the PCG solver may obtain a product by multiplying the matrix S bythe vector X₀, and then subtract the product of the matrix S and thevector X₀ from the vector b. In other words, the PCG solver may obtain avalue by multiplying the matrix S by the vector X₀ and then multiplyingby −1, and then add the value to the vector b. r₀ may denote a residualvector.

Referring to FIG. 7, the PCG solver may perform a mathematical operationusing a preconditioner. In operation 703, the PCG solver may multiply aninverse M⁻¹ of the preconditioner M by the residual vector r₀. Theinverse M⁻¹ of the preconditioner M may serve as a linear operator. Forexample, a product of the multiplication of the inverse M⁻¹ of thepreconditioner M by the residual vector r₀ may equal a preconditionedresidual vector z₀. The precondition residual vector z₀ may equal asearch direction vector p₀. The search direction vector p₀ may determinea direction in which repeatability is made in performing all repeatingoperations.

Referring to FIG. 7, in operation 704, the PCG solver may multiply atranspose r_(k) ^(T) of a kth residual vector by a kth preconditionedresidual vector z_(k). In operations 705, the PCG solver may multiplythe matrix S by a kth search direction vector p_(k).

Referring to FIG. 7, the PCG solver may calculate a scalar α fordetermining a length of a step to be taken along a search directiontoward a solution. For example, the PCG solver may multiply a transposep_(k) ^(T) of the kth search direction vector by a product calculated inoperation 705 (e.g., p_(k) ^(T)Sp_(k)). In operation 706, the PCG solvermay divide a result value obtained in operation 704, by a value obtainedby calculating p_(k) ^(T)Sp_(k). A quotient obtained in 706 maycorrespond to a kth scalar α_(k).

Referring to FIG. 7, the PCG solver may perform calculation related to arepetitive vector X. For example, in operation 707, the PCG solver maycalculate a (k+1)th repetitive vector X_(k+1). The (k+1)th repetitivevector X_(k+1) may correspond to a value obtained by adding, to a kthrepetitive vector X_(k), a product of the kth scalar α_(k) and the kthsearch direction vector p_(k).

Referring to FIG. 7, the PCG solver may perform calculation related to aresidual vector r. For example, in operation 708, the PCG solver maycalculate a (k+1)th residual vector r_(k+1). The (k+1)th residual vectorr_(k+1) may correspond to a value obtained by subtracting, from the kthresidual vector r_(k), a product obtained by multiplying the kth scalarα_(k) by the matrix S, and then by the kth search direction vectorp_(k).

Referring to FIG. 7, the PCG solver may compare the (k+1)th residualvector r_(k+1) with a threshold e_(threshold). For example, in operation709, the PCG solver may determine whether a magnitude of the (k+1)thresidual vector r_(k+1) is less than the threshold e_(threshold).

Referring to FIG. 7, in a case where the magnitude of the (k+1)thresidual vector r_(k+1) has been determined to be greater than or equalto the threshold e_(threshold), the PCG solver may perform operation710. For example, the PCG solver may calculate a (k+1)th preconditionedresidual vector z_(k+1) by multiplying the inverse M⁻¹ of thepreconditioner M by the (k+1)th residual vector r_(k+1).

Referring to FIG. 7, the PCG solver may perform calculation of a scalarβ used for conjugation of a search direction. The PCG solver maycalculate a (k+1)th result value by multiplying the (k+1)thpreconditioned residual vector z^(T) _(K+1) by the (k+1)th residualvector r_(k+1). The PCG solver may calculate a kth result value bymultiplying a kth preconditioned residual vector z^(T) _(k) by the kthresidual vector r_(k). In operation 711, the PCG solver may calculate akth scalar β_(k) by dividing the (k+1)th result value by the kth resultvalue.

Referring to FIG. 7, the PCG solver may perform calculation of a (k+1)thsearch direction vector p_(k+1). For example, in operation 712, the PCGsolver may calculate the (k+1)th search direction vector p_(k+1) byadding the (k+1)th preconditioned residual vector z_(k+1), to a productobtained by multiplying the kth scalar β_(k) by the kth search directionvector p_(k).

Referring to FIG. 7, in operation 713, the PCG solver may increment kby 1. In a case where the magnitude of the (k+1)th residual vectorr_(k+1) has been determined to be lower than the threshold ethreshold inoperation 709, the PCG solver may perform operation 714 to output the(k+1)th repetitive vector X_(k+1).

FIG. 8 is an exemplary diagram related to mathematical operationsperformed by the PCG solver 200 and their outputs, according to variousembodiments.

An example shown in FIG. 8 may include the mathematical operationsperformed by the matrix-vector multiplier 220, and addition operationsperformed after the multiplication operation of a matrix and a vector.Mathematical operations 800 of the PCG solver may include arithmeticoperations performed on a matrix and a matrix, a matrix and a vector, avector and a vector, and a vector and a scalar.

Referring to FIG. 8, the back-end processor (e.g., the back-endprocessor 110 of FIG. 1) of the PCG solver may configure a matrix 810according to the factors. The matrix 810 may have a size of 75*75, and alarger hatched area defined by the solid lines in a row block 811 maydepict a submatrix having a size of 15*15. A smaller hatched area in therow block 811 may depict a submatrix having a size of 6*6 and may berelated to a position and a rotation among the six degrees offreedom-related components. A dotted area defined by the solid linesother than the smaller hatched area in the row block 811 may depict asubmatrix defined by excluding the submatrix of the smaller hatched areafrom the 15*15 submatrix. The submatrix depicted by the dotted area mayinclude triaxial components for an IMU velocity, an IMU acceleration,and an IMU angular velocity. Descriptions of a size and included areasof a column block 812 may be replaced with the descriptions of the rowblock 811.

Referring to FIG. 8, the PCG solver (e.g., the PCG solver 100 of FIG. 1or the PCG solver 200 of FIG. 2) may perform calculation for each rowblock 811 of the matrix 810 in order to rapidly process themultiplication operations of a matrix and a vector. The PCG solver mayaccess data of a maximum size for each row, on which calculation isperformed, such that the calculation may be performed on transposeelements as well at once. The column block 812 may correspond to thetranspose elements, and thus the mathematical operations may beminimized. For the mathematical operations performed on the vector, thePCG solver may access each element of the vector as many times as itssize, to sequentially perform the mathematical operations, and thenshift to access a next element.

The example shown in FIG. 8 may correspond to the mathematicaloperations with a maximum track size set as 5. A number ofmultiplication operations, that is, equal to the maximum track size, maybe performed on a submatrix and each element of the vector. For eachrow, the calculation may be performed on the transpose elements as wellat once. Referring to FIG. 8, data corresponding to result values of themultiplication and addition operations of the matrix 810 and the vectormay be stored in an output vector 830. In the mathematical operationswith respect to the row block, products of elements of the submatrix andthe vector may be calculated, then an addition operation may beperformed on the products, and resulting sums may be stored in a firstoutput subvector 831. An individual subvector may have a size of 15*1.The transpose elements may be calculated with the vector, and thenresult values may be stored in second to fifth output subvectors 832,respectively. When a corresponding mathematical operation is performedfor each row, calculation results calculated for the transpose elementsmay be accumulated, and when a current row becomes the first row, thecalculation may be finished and output vectors for the corresponding rowmay be derived as result values.

FIG. 9 is an exemplary diagram related to mathematical operationsimplification and resulting outputs of the PCG solver 200, according tovarious embodiments.

An example 800 shown in FIG. 9 may be the same as the example shown inFIG. 8 and may correspond to an example for accelerating mathematicaloperation processes. The PCG solver (e.g., the PCG solver 100 of FIG. 1or the PCG solver 200 of FIG. 2) may access and process fifteen-linedata 911 of a component 910 (e.g., a 15*15 submatrix) of each row blockat once by accessing a plurality of lines. Processing at once may meanthat the mathematical operations are performed at once. Data related tothe six degrees of freedom-related components excluding IMU-relatedcomponents, from among fifteen pieces of data, may be a 6*6 block, andthus corresponding blocks may be collected and then processed at once.Referring to FIG. 9, the PCG solver may process three lines at once, andthe mathematical operations may also be simultaneously performed onthree lines of the transpose elements.

Referring to FIG. 9, products and sums calculated from the matrix andthe vector may be stored in a column vector. The column vector may haveindividual blocks of a size of 15*15. For example, components 930 of theindividual block may correspond to a position, a rotation, a linearvelocity, an acceleration, and an angular velocity. R_(xn), R_(yn) andR_(zn) may be the six degrees of freedom-related components. R_(xn) maybe a rotation component with respect to the x axis, R_(yn) may be arotation component with respect to the y axis, and R_(zn) may be arotation component with respect to the z axis, from among the sixdegrees of freedom-related components. T_(xn), T_(yn), and T_(zn) may bethe six degrees of freedom-related components. T_(xn) may be a positioncomponent with respect to the x axis, T_(yn) may be a position componentwith respect to the y axis, and T_(zn) may be a position component withrespect to the z axis, from among the six degrees of freedom-relatedcomponents.

Referring to FIG. 9, the components 930 of the individual block may bethe six degrees of freedom-related components (in particular,IMU-related components). For example, V_(xn), V_(yn), and V_(zn) may belinear velocity-related components among the six degrees offreedom-related components. V_(xn) may be a linear velocity componentwith respect to the x axis, V_(yn) may be a linear velocity componentwith respect to the y axis, and V_(zn) may be a linear velocitycomponent with respect to the z axis, from among the six degrees offreedom-related components. Ba_(xn), Ba_(yn), and Ba_(zn) may beacceleration-related components among the six degrees of freedom-relatedcomponents. Ba_(xn) may be an acceleration component with respect to thex axis, Ba_(yn) may be an acceleration component with respect to the yaxis, and Ba_(zn) may be an acceleration component with respect to the zaxis, from among the six degrees of freedom-related components. Bg_(xn),Bg_(yn), and Bg_(zn) may be angular velocity-related components amongthe six degrees of freedom-related components. Bg_(xn) may be an angularvelocity component with respect to the x axis, Bg_(yn) may be an angularvelocity component with respect to the y axis, and Bg_(zn) may be anangular velocity component with respect to the z axis, from among thesix degrees of freedom-related com ponents.

A preconditioned conjugate gradient (PCG) solver, embedded in anelectronic device to perform a simultaneous localization and mapping(SLAM) operation, may include an image database, a factor graphdatabase, and a back-end processor, wherein the back-end processor isconfigured to receive an image from the image database to performre-localization, receive, from the factor graph database, data forcalculating six degrees of freedom (DoF)-related components, construct amatrix including the six degrees of freedom-related components based onthe received data, and load and rearrange the matrix and a vector, toperform calculation on each block of each row of the matrix and thevector, then output first data, and shift second data to a location ofthe first data.

A back-end processor of the PCG solver performing the SLAM operation mayreuse as many elements as a size of the block in the calculation of thematrix and the vector.

The back-end processor of the PCG solver performing the SLAM operationmay calculate only diagonal elements of the matrix by using propertiesof a scattering matrix (S matrix).

The back-end processor of the PCG solver performing the SLAM operationmay also calculate as many transpose elements as a maximum size of eachrow block in the calculation performed on each block of each row of theconstructed matrix.

The back-end processor of the PCG solver performing the SLAM operationmay output the shifted second data, and accumulate and output the seconddata together with the first data.

The back-end processor of the PCG solver performing the SLAM operationmay simultaneously perform the accumulating of the first data and theshifting of the second data.

The back-end processor of the PCG solver performing the SLAM operationmay perform the shifting of the second data by using a shift register.

Elements of the matrix constructed by the PCG solver performing the SLAMoperation may include position, rotation, linear velocity, acceleration,and angular velocity components with respect to three axes of theelectronic device.

The back-end processor of the PCG solver performing the SLAM operationmay control an interval between the outputting of the first data and theoutputting of the second data according to a preset period.

The image database of the PCG solver performing the SLAM operation maystore an image received from a camera of the electronic device.

A method of accelerating simultaneous localization and mapping (SLAM)performed by a preconditioned conjugate gradient (PCG) solver embeddedin an electronic device, may include receiving an image from an imagedatabase to perform re-localization, receiving, from a factor graphdatabase, data for calculating six degrees of freedom (DoF)-relatedcomponents, constructing a matrix including the six degrees offreedom-related components based on the received data, and loading andrearranging the matrix and a vector, to perform calculation on eachblock of each row of the matrix and the vector, then output first data,and shift second data to a location of the first data.

The method of accelerating simultaneous localization and mapping (SLAM)performed by a preconditioned conjugate gradient (PCG) solver mayfurther include reusing as many elements as a size of the block in thecalculation performed on the matrix and the vector.

The method of accelerating simultaneous localization and mapping (SLAM)performed by a preconditioned conjugate gradient (PCG) solver mayfurther include calculating only diagonal elements of the matrix byusing properties of a scattering matrix.

The method of accelerating simultaneous localization and mapping (SLAM)performed by a preconditioned conjugate gradient (PCG) solver mayfurther include calculating as many transpose elements as a maximum sizeof each row block in the calculation performed on each block of each rowof the constructed matrix.

The method of accelerating simultaneous localization and mapping (SLAM)performed by a preconditioned conjugate gradient (PCG) solver mayfurther include outputting the shifted second data, and accumulating andoutputting the second data together with the first data.

The outputting of the second data in the method of acceleratingsimultaneous localization and mapping (SLAM) performed by apreconditioned conjugate gradient (PCG) solver may includesimultaneously performing the accumulating of the first data and theshifting of the second data.

The method of accelerating simultaneous localization and mapping (SLAM)performed by a preconditioned conjugate gradient (PCG) solver mayfurther include performing the shifting of the second data by using ashift register.

The constructing of the matrix in the method of acceleratingsimultaneous localization and mapping (SLAM) performed by apreconditioned conjugate gradient (PCG) solver may include calculatingposition, rotation, velocity, acceleration, and angular velocitycomponents with respect to three axes of the electronic device.

The method of accelerating simultaneous localization and mapping (SLAM)performed by a preconditioned conjugate gradient (PCG) solver mayfurther include controlling an interval between the outputting of thefirst data and the outputting of the second data according to a presetperiod.

The method of accelerating simultaneous localization and mapping (SLAM)performed by a preconditioned conjugate gradient (PCG) solver mayfurther include storing, in the image database, an image received from acamera of the electronic device.

As a processing speed of mathematical operations of the back-endprocessor increases, time required for performing an overall operationof SLAM may be shortened. In a case of performing a multiplicationoperation on a matrix and a vector requiring a large amount ofoperation, the back-end processor may increase a processing speed of theoperation by using properties of an S matrix.

The back-end processor of a preconditioned conjugate gradient (PCG)solver may be configured in various devices to prevent data transmissionand reception delay. In a case of a low-power, low-performance back-endprocessor, a size and power consumption of the device in which theback-end processor is embedded may be reduced.

While not restricted thereto, an example embodiment can be embodied ascomputer-readable code on a computer-readable recording medium. Thecomputer-readable recording medium is any data storage device that canstore data that can be thereafter read by a computer system. Examples ofthe computer-readable recording medium include read-only memory (ROM),random-access memory (RAM), CD-ROMs, magnetic tapes, floppy disks, andoptical data storage devices. The computer-readable recording medium canalso be distributed over network-coupled computer systems so that thecomputer-readable code is stored and executed in a distributed fashion.Also, an example embodiment may be written as a computer programtransmitted over a computer-readable transmission medium, such as acarrier wave, and received and implemented in general-use orspecial-purpose digital computers that execute the programs. Moreover,it is understood that in example embodiments, one or more units of theabove-described apparatuses and devices can include circuitry, aprocessor, a microprocessor, etc., and may execute a computer programstored in a computer-readable medium.

The foregoing exemplary embodiments are merely exemplary and are not tobe construed as limiting. The present teaching can be readily applied toother types of apparatuses. Also, the description of the exemplaryembodiments is intended to be illustrative, and not to limit the scopeof the claims, and many alternatives, modifications, and variations willbe apparent to those skilled in the art.

What is claimed is:
 1. An electronic device to perform a simultaneouslocalization and mapping (SLAM) operation, the electronic devicecomprising: an image database; a factor graph database; and a processorconfigured to: receive, from the image database, a map image in which aposition of the electronic device is localized, to performre-localization of the position of the electronic device in the mapimage; receive, from the factor graph database, data for calculating sixdegrees of freedom (DoF)-related components of the electronic device;construct a matrix including the six DoF-related components based on thereceived data; and load and rearrange the matrix and a vector that isselected from a plurality of vectors stored in a memory, to sequentiallyobtain first data and second data by performing calculation on eachblock of each row of the matrix and the vector, and shift the seconddata to a storage location of the first data.
 2. The electronic deviceof claim 1, wherein the processor is further configured to reuse as manyelements as a size of the block in the calculation of the matrix and thevector.
 3. The electronic device of claim 1, wherein the processor isfurther configured to calculate only diagonal elements of the matrix byusing properties of a scattering matrix that is derived from the mapimage and the data for calculating the six DoF-related components. 4.The electronic device of claim 1, wherein the processor is furtherconfigured to calculate as many transpose elements as a maximum size ofeach row block in the calculation performed on each block of each row ofthe constructed matrix.
 5. The electronic device of claim 1, wherein theprocessor is further configured to output the shifted second data, andaccumulate the second data and the first data.
 6. The electronic deviceof claim 5, wherein the processor is further configured tosimultaneously perform accumulation of the first data and the seconddata, and shifting of the second data.
 7. The electronic device of claim6, wherein the processor is further configured to perform the shiftingof the second data by using a shift register.
 8. The electronic deviceof claim 1, wherein elements of the constructed matrix include aposition component, a rotation component, a linear velocity component,an acceleration component, and an angular velocity component withrespect to three axes of the electronic device.
 9. The electronic deviceof claim 1, wherein the processor is further configured to control aninterval between a first output time of the first data and a secondoutput time of the second data according to a preset period.
 10. Theelectronic device of claim 1, wherein the image database stores an imagereceived from a camera of the electronic device.
 11. A method ofaccelerating simultaneous localization and mapping (SLAM) performed byan electronic device, the method comprising: receiving, from an imagedatabase, a map image in which a position of the electronic device islocalized, to perform re-localization of the position of the electronicdevice in the map image; receiving, from a factor graph database of theelectronic device, data for calculating six degrees of freedom(DoF)-related components of the electronic device; constructing a matrixincluding the six DoF-related components based on the received data; andloading and rearranging the matrix and a vector that is selected from aplurality of vectors stored in a memory, to sequentially obtain firstdata and second data by performing calculation on each block of each rowof the matrix and the vector, and then shift the second data to astorage location of the first data.
 12. The method of claim 11, furthercomprising reusing as many elements as a size of the block in thecalculation performed on the matrix and the vector.
 13. The method ofclaim 11, further comprising calculating only diagonal elements of thematrix by using properties of a scattering matrix that is derived fromthe map image and the data for calculating the six DoF-relatedcomponents.
 14. The method of claim 11, further comprising calculatingas many transpose elements as a maximum size of each row block in thecalculation performed on each block of each row of the constructedmatrix.
 15. The method of claim 11, further comprising outputting theshifted second data, and accumulating the second data and the firstdata.
 16. The method of claim 15, wherein the outputting of the seconddata includes simultaneously performing accumulation of the first dataand the second data, and shifting of the second data.
 17. The method ofclaim 16, further comprising performing the shifting of the second databy using a shift register.
 18. The method of claim 11, wherein theconstructing of the matrix includes calculating a position component, arotation component, a linear velocity component, an accelerationcomponent, and an angular velocity component of the matrix with respectto three axes of the electronic device.
 19. The method of claim 11,further comprising controlling an interval between a first output timeof the first data and a second output time of the second data accordingto a preset period.
 20. The method of claim 11, further comprisingstoring, in the image database, the map image that is generated based onan image received from a camera of the electronic device.